Audio released by Abdullah Abdullah's campaign allegedly capture senior election official conspiring with team of rival candidate Ashraf Ghani

Sheep at a Kabul livestock market. In the recordings, one man says: 'Take the sheep into the mountain and bring them back stuffed', referring to illegally filled ballot boxes. Photograph: Muhammed Muheisen/AP

Afghanistan's leadership crisis has deepened after one presidential candidate released audio recordings that he said captured a senior election official conspiring to commit large-scale fraud using the code word "stuffed sheep" to discuss illegally filled ballot boxes.

In 15 minutes of sometimes slightly surreal conversation, two men urge an official to fire election staff with suspect loyalties and replace them with known supporters, ramp up plans for vote buying and ballot stuffing, and close down polling stations in areas thought to be unsympathetic.

"Take the sheep into the mountain and bring them back stuffed," one man says, before apparently lamenting the growing cost of buying votes. "The price of goats and sheep has gone up these days," he says ruefully.

A campaign manager for former mujahideen doctor Abdullah Abdullah on Sunday said one speaker in that conversation was a close aide of the country's chief electoral officer, Ziaulhaq Amarkhil, although he refused to reveal the source of the recordings or offer any verification of the speakers' identity.

He claimed that the other man was from the campaign team of Ashraf Ghani, a former World Bank technocrat and author of the book Fixing Failed States. Ghani appears to have a majority of votes in the 14 June run-off against Abdullah but is accused by his rival of cheating.

A two-stage vote that was initially hailed as a triumph for the Afghan people and their fledging democracy, after Taliban threats failed to deter millions from turning out to cast their ballots, has since descended into a tense standoff with no clear path to a resolution.

Abdullah announced last week that he was withdrawing from the election process, accusing incumbent Hamid Karzai and Amarkhil of helping Ghani rig the vote, with assistance from government and election officials around the country.

He called for United Nations mediation, an offer unexpectedly endorsed by Karzai himself, even though the president had spent years squeezing all traces of foreign influence out of the electoral system. The UN itself has been more circumspect.

"This is a process which we respect as an Afghan-led process, Afghan-managed process and we would not want to take steps which would be seen as interfering or substituting the UN for Afghan leadership," deputy UN envoy Nicholas Haysom told journalists on Saturday.

"The task ahead of us is to have the candidates re-engage fully in the electoral process … There is no other way of electing a legitimate leader."

The UN has not been given a copy of the phone conversations but has urged Abdullah's team to submit the recording to officials monitoring fraud, spokesman Ari Gaitanis said.

Amarkhil himself was allegedly captured in some of the conversations played to journalists, asking a contact to "bring the sheep, stuffed properly", but also complaining peevishly about how little attention Ghani was giving him.

Abdullah's team had already complained to media about Amarkhil, and his photograph was burned at anti-fraud demonstrations called by Abdullah's supporters at the weekend.

Amarkhil, a former UN employee, denied that he had meddled in the election or that the audio recordings captured his conversations. "I would never talk like that," he told the Wall Street Journal. Spokesmen for Ghani and the election commission, in interviews broadcast on Afghan TV, questioned both the authenticity of the recordings and how they had been obtained.